* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Given that Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given the rugged terrain of Ngazidja and Nzwani, and the dedication of extensive tracts to agriculture on all three islands, population pressures on Comoros are becoming increasingly critical.

Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A

Given its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.

* Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition ‡;

* Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits of G.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given the great historical link between Persian and Jewish history, modern day Persian Jews are called " Esther's Children ".

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

Given their hunting instincts, they are prone to chasing moving objects.

Given that the cable was laid on the surface of the seabed it was prone to being fouled by fishing nets, causing damage.

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given an object X, a functor G ( taking for simplicity the first functor to be the identity ) and an isomorphism proof of unnaturality is most easily shown by giving an automorphism that does not commute with this isomorphism ( so ).

Given these rates, Spanish employers who do hire interns often may be taking advantage of unpaid interships in order to get free labor.

Given a function on, one may " geometrize " it by taking it to define a new manifold.

Given certain legal traditions of copyright, blogs may not be " open source " in the sense that one is prohibited from taking the blogger's words or visitor comments and re-using them in another form without breaching the author's copyright or making payment.

Lessig traces the simultaneous legal environment that permitted its genious: Given the challenge of deciding whether photographers would need to get per mission before taking aim, the legal system decided " in favor of the pirates .....

Given these family hardships, Myers began taking odd jobs at a young age, living in Baltimore, Maryland, before moving on to New York City.

Given that her lord's kinsmen ( þæt monnes magas ) are described as taking measures to separate the speaker from him, a probable interpretation of the speaker's initial circumstances is that she has been entered into an exogamous relationship typical within the Anglo-Saxon heroic tradition, and her marital status has left her isolated among her husband's people, who are hostile to her, whether due to her actions or merely due to political strife beyond her control.

Given an interior algebra we can form the Stone representation of its underlying Boolean algebra and then extend this to a topological field of sets by taking the topology generated by the complexes corresponding to the open elements of the interior algebra ( which form a base for a topology ).

Given a choice of staying behind and seeing her son and maybe having him work for her, leaving and never seeing her son again, or taking the drug and becoming a fellow addict, the mother asks Neal what he thinks she should do.

Given, one could efficiently decide whether by first taking the discrete of, and then comparing with.

* Rush Limbaugh: Given on March 5, 2009, for taking a modest mention by the president and turning it into media gold.

Given the Seventh Doctor's appearance and stature, he was surprisingly capable of both directly and indirectly taking control of situations involving strangers, using his greater intelligence to assess and direct events.

Given the backdrop of what was taking place in Northern Ireland when the UVF bombing republican targets at will, either the researchers decided to take poetic licence to the limit or the truth was being twisted by knaves to make trap for the fools.

Given a knot K in the 3-sphere, it has a Seifert surface S whose boundary is K. The Seifert form of S is the pairing given by taking the linking number where and indicate the translates of a and b respectively in the positive and negative directions of the normal bundle to S.

Given the multifinality of psychopathological disorders, two children may be on the same medication for two completely different disorders, or have the same disorder and be taking two completely different medications.

Given the size of the project, construction progressed quickly, taking just two years.

Given the title of the play, and taking a cue from the aetiology for the Athenian Areopagus provided by Aeschylus ' Eumenides, it has been suggested that the drama concludes with Zeus ' foundation of the yearly torch race that took place in Athens to honor Prometheus.

Others included a penalty shootout with goalkeeper Shay Given at Newcastle United ; taking on Ken Doherty in snooker ; and, most recently, spending time with Aidan O ' Brien, one of the world's most successful race horse trainers.

Given the dire employment situation in the early 1930s, Emeneau stayed on at Yale after completing his dissertation, taking courses in the " new linguistics " being taught by Edward Sapir.